Dynamic range shows the ratio of a specified maximum level of a parameter to the minimum detectable value of that parameter. High dynamic range imaging allows a greater dynamic range of exposures than normal digital imaging techniques. For example, a high dynamic range image can accurately represent the wide range of intensity levels found in real scenes, ranging from direct sunlight to the dark shadows. In a normal digital imaging technique, either the dark region or the bright region becomes saturated, or almost saturated, so that the details in these regions become unrecognizable.
Typically, a digital camera has a limited dynamic range. With a given exposure setting, the digital camera may not be able to capture the details in a bright area in the scene, since the bright area in the picture taken by the digital camera is saturated and represented as a uniform white region. Similarly, the details in a dark area in the scene may be captured as a uniform black region. Increasing the exposure duration may allow the camera to capture more details in the dark region but lose more details near the bright region as the bright region expands. Reducing the exposure duration may allow the camera to capture more details in the bright region but lose more details near the dark region as the dark region expands.
Paul E. Debevec and Jitendar Malik (Recovering high dynamic range radiance maps from photographs, Proc. of SIGGRAPH 97, Computer Graphics Proceedings, Annual Conference Series, pp. 369-378, 1997), presents a method to derive a response curve that relates the pixel image values and the natural logarithm of the product of irradiance and exposure duration. The response curve then can be used to recover high dynamic range radiance maps from series of images of a same scene taken at different exposure levels. In one example, Paul E. Debevec and Jitendar Malik map the logarithm of the radiance values into a gray scale image, which presents all the information in the series of images taken at the different exposure levels.
To obtain the response curve, Paul E. Debevec and Jitendar Malik formulated a quadratic objective function for least square minimization. The minimization process is formulated to solve for both the response curve and for the irradiances involved simultaneously. The quadratic objective function involves the second derivative of the response curve in order to obtain a smooth response curve.